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A recent paper
by Alessandro Bonanno and Stephan Goetz in the International Food and Agribusiness Management Review looks at the
relationship between food store density, nutrition education, and obesity.

Here is the issue:

Understanding the role of the food environment vs. nutrition
education in expanding the share of adult population engaging in healthy eating
habits has clear policy implications and is relevant for the agribusiness
sector as a whole. Food retailers and
food service companies, as well as many food manufacturers, are under scrutiny
for their potential roles in shaping diets and in contributing to the obesity
epidemic. This study seeks to provide additional evidence on whether policies
aimed at regulating the food environment (i.e., the location of food retailers
and restaurants) are likely to achieve the intended goals

They find:

no evidence of a negative
causal relationship between the density of food-service establishments
and the state-level incidence of adult healthy eating (similar to Collins and
Baker, 2009, who find no “Granger causality” on obesity incidence using
nationwide data), suggesting that policies aiming to restrict access to these
outlets may have little impact on improving healthy diets.

And:

Our results indicate that expenditures on nutrition
education programs can improve eating habits and, indirectly, curb the
incidence of adult obesity. However,
increases in nutrition education efforts would have to be substantial. . . . our
results indicate that quadrupling average expenditure on nutrition education .
. . could reduce adult obesity by 0.8%; the feasibility of such a large
spending increase as a policy tool is unlikely